Train A crosses a pole and platform in 18 secnds and 39 seconds respectively. The length of platform is 157.5 metre. What will be the length of train B if it is equal to the sum of half of the length of train A and twice the length of the platform?

Let length of train A = $$l$$ metres

and speed of train A = $$x$$ m/s

Using, $$time = \frac{distance}{speed}$$

=> $$\frac{l}{x} = 18$$

=> $$x = \frac{l}{18}$$

Length of platform = $$157.5$$ metres

=> $$\frac{157.5 + l}{x} = 39$$

Substituting value of $$x$$, we get :

=> $$\frac{157.5 + l}{39} = \frac{l}{18}$$

=> $$13l = 6l + 945$$

=> $$13l - 6l = 7l = 945$$

=> $$l = \frac{945}{7} = 135$$ metres

$$\therefore$$ Length of train B

= $$(\frac{135}{2}) + (157.5 \times 2)$$

= $$67.5 + 315 = 382.5$$ metres